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THE UNITY AND IDENTITY OF DECIDABLE OBJECTS AND DOUBLE-NEGATION SHEAVES

Published online by Cambridge University Press:  21 December 2018

MATÍAS MENNI
MATÍAS MENNI*
Affiliation:
CONICET AND UNIVERSIDAD NACIONAL DE LA PLATA LA PLATA1900ARGENTINAE-mail: [email protected]
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Abstract

Let ${\cal E}$ be a topos, ${\rm{Dec}}\left( {\cal E} \right) \to {\cal E}$ be the full subcategory of decidable objects, and ${{\cal E}_{\neg \,\,\neg }} \to {\cal E}$ be the full subcategory of double-negation sheaves. We give sufficient conditions for the existence of a Unity and Identity ${\cal E} \to {\cal S}$ for the two subcategories of ${\cal E}$ above, making them Adjointly Opposite. Typical examples of such ${\cal E}$ include many ‘gros’ toposes in Algebraic Geometry, simplicial sets and other toposes of ‘combinatorial’ spaces in Algebraic Topology, and certain models of Synthetic Differential Geometry.

Keywords

18B2518F9903E99axiomatic cohesiontopos theoryset theory
Type
Articles
Information
The Journal of Symbolic Logic , Volume 83 , Issue 4 , December 2018 , pp. 1667 - 1679
Copyright
Copyright © The Association for Symbolic Logic 2018 

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